Mathematical Sciences: Topics in Ergodic Theory and Analysis

数学科学：遍历理论与分析主题

• 批准号: 9303327
• 负责人: Alexandra Bellow
• 金额: $ 6.55万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303327&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Ergodic; Theory

Bellow will study almost everywhere convergence in analysis and ergodic theory. She will investigate questions concerning almost everywhere convergence for absolutely integrable functions, the central limit theorem on the real line and its transference to the ergodic setting, and questions related to the solution of an old problem of Hopf. Singular integral techniques will be further developed and applied. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

Because 遍历理论。 她将调查有关 绝对可积的几乎处处收敛 函数，真实的直线上的中心极限定理及其 转移到遍历设置，以及与 一个老问题的解决方案。 奇异积分技术 将得到进一步发展和应用。 这个项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 系统的动力学过于复杂或混乱， 在微观细节上进行跟踪。 在“动态”标题下， 可以把现代理论放在抽象的 变换作用于光滑空间。 这样遍历理论 与几何学接触，以寻求对 齐性空间